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C₄×#3415 #7622615

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1996 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 36 points:

(1,2,3,4);(5,6)(7,12)(8,11)(9,22)(10,15)(13,19)(14,20)(16,26)(17,23)(18,32)(21,25)(24,33)(27,31)(28,30)(29,34)(35,36);(6,11)(8,19)(9,20)(12,23)(13,14)(15,25)(17,31)(18,30)(21,33)(22,24)(26,34)(27,28)(29,36)(32,35);(5,7)(6,12)(8,17)(9,18)(10,16)(11,23)(13,27)(14,28)(15,26)(19,31)(20,30)(21,29)(22,32)(24,35)(25,34)(33,36);(7,16)(12,26)(17,29)(18,30)(23,34)(27,35)(28,32)(31,36)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529811);